For FFT the confusing part is that it's using much longer time interval than what is displayed on the screen. That is the only way one can get a fine frequency resolution with just 4 periods on the screen.
Yes, in the video, the FFT is clearly using a window that is 10-100x larger than the screen (and more than the claimed 4 kpts of memory as well). Naturally that also increases the chance that the glitch fall in this window and show up in the spectrum. Having the spectrum analysis tool mostly independent from the time-domain view adds a lot of flexibility but may also be confusing at first. There appears to be a "Gate" sub-menu, so I am assuming you can still do time-domain correlated analysis as well.
One somewhat disappointing aspect is the apparent lack of analysis features. This oscilloscope has huge memory but once you have filled it, there doesn't seem to be much that you can do with it. Things like trigger event and outlier search, measurement tracks, anything that could help you find regions of interest without trying to scroll through 800 Mpts manually. Can you at least search the protocol decodes after the fact (using the filter tab I guess)?